9.7 Semiconductor devices  (Page 2/12)

We can estimate the mathematical relationship between the current and voltage for a diode using the electric potential concept. Consider N negatively charged majority carriers (electrons donated by impurity atoms) in the n -type material and a potential barrier V across the p-n junction. According to the Maxwell-Boltzmann distribution, the fraction of electrons that have enough energy to diffuse across the potential barrier is $N{e}^{\text{−}eV\text{/}{k}_{\text{B}}T}$ . However, if a battery of voltage $V_b$ is applied in the forward-bias configuration, this fraction improves to $N{e}^{\text{−}e\left(V-V_b\right)\text{/}{k}_{\text{B}}T}$ . The electric current due to the majority carriers from the n -side to the p -side is therefore

where $I_0$ is the current with no applied voltage and T is the temperature. Current due to the minority carriers (thermal excitation of electrons from the valence band to the conduction band on the p- side and subsequent attraction to the n -side) is $\text{−}{I}_0$ , independent of the bias voltage. The net current is therefore

A sample graph of the current versus bias voltage is given in [link] . In the forward bias configuration, small changes in the bias voltage lead to large changes in the current. In the reverse bias configuration, the current is $I_{\text{net}}\approx \text{−}{I}_0$ . For extreme values of reverse bias, the atoms in the material are ionized which triggers an avalanche of current. This case occurs at the breakdown voltage    .